Abstract
Sometimes fingerprint-like features are found in a material. The exciting discovery poses new challenges on how to use the features to build an object authentication protocol that could tell customers and retailers equipped with a mobile device whether a good is authentic or fake. We are exactly in this situation with Cholesteric Spherical Reflectors (CSRs), tiny spheres of liquid crystals with which we can tag or coat objects. They are being proposed as a potential game-changer material in anti-counterfeiting due to their unique optical properties. In addition to the problem of processing images and extracting the minutiæ embedded in a CSR, one major challenge is designing cryptographically secure authentication protocols. The authentication procedure has to handle unstable input data; it has to measure the distance between some reference data stored at enrollment and noisy input provided at authentication. We propose a cryptographic authentication protocol that solves the problem, and that is secure against semi-honest and malicious adversaries. We prove that our design ensures data privacy even if enrolled data are leaked and even if servers and provers are actively curious. We implement and benchmark the protocol in Python using the Microsoft SEAL library through its Python wrapper PySEAL.
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Notes
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Match and mismatch will be defined over the features metric space.
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- 3.
“Random” is intended informally, meaning “in a way that we cannot anticipate”.
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It is a means on the values of blobs, and it returns \(\bot \) when one of the elements is \(\bot \).
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Here, the number of pictures that a User takes in the enrollment and authentication can be defined by the process. We used five images in our implementation, see Sect. 5.
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References
Albrecht, M.R., et al.: Homomorphic Encryption Standard. IACR, p. 939 (2019). Cryptol. ePrint Arch. https://eprint.iacr.org/2019/939
Arenas, M., Demirci, H., Lenzini, G.: Cholesteric spherical reflectors as physical unclonable identifiers in anti-counterfeiting. In: The 16th International Conference on Availability, Reliability and Security, pp. 1–11. ACM (2021). https://doi.org/10.1145/3465481.3465766
Arenas, M., Demirci, H., Lenzini, G.: An analysis of cholesteric spherical reflector identifiers for object authenticity verification. Mach. Learn. Knowl. Extr. 4(1), 222–239 (2022). https://doi.org/10.3390/make4010010
Bai, Z., Hatzinakos, D.: LBP-based biometric hashing scheme for human authentication. In: 11th International Conference on Control Automation Robotics Vision (ICARCV), pp. 1842–1847 (2010). https://doi.org/10.1109/ICARCV.2010.5707216
Bicego M., Lagorio, A., Grosso, E., Tistarelli, M.: On the use of SIFT features for face authentication. In: Conference On Computer Vision And Pattern Recognition Workshop. CVPRW 2006, pp. 35–35 (2006)
Bicer, O., Bingol, M.A., Kiraz, M., Levi, A.: Highly efficient and re-executable private function evaluation with linear complexity. IEEE Trans. Dependable Secure Comput. 19(02), 835–847 (2022). https://doi.org/10.1109/TDSC.2020.3009496
Bingol, M.A.: Efficient and secure schemes for private function evaluation. Ph.D. thesis, Sabanci University, Istanbul (2019). https://research.sabanciuniv.edu/id/eprint/36861/
Boddeti, V.N.: Secure face matching using fully homomorphic encryption. In: 2018 IEEE 9th International Conference on Biometrics Theory, Applications and Systems (BTAS), pp. 1–10. IEEE (2018)
Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) Advances in Cryptology - CRYPTO 2012–32nd Annual Cryptology Conference, Santa Barbara, CA, USA, 19–23 August 2012. Proceedings. Lecture Notes in Computer Science, vol. 7417, pp. 868–886. Springer (2012). https://doi.org/10.1007/978-3-642-32009-5_50
Deledalle, C.A., Denis, L., Tupin, F.: How to compare noisy patches? Patch similarity beyond gaussian noise. Int. J. Comput. Vision, 99(1), 86–102 (2012). https://doi.org/10.1007/s11263-012-0519-6, https://hal-imt.archives-ouvertes.fr/hal-00672357, http://link.springer.com/10.1007/s11263-012-0519-6
Fan, J., Vercauteren, F.: Somewhat Practical Fully Homomorphic Encryption (2012). https://ia.cr/2012/144. Cryptology ePrint Archive, Report 2012/144
Geng, Y., Noh, J., Drevensek-Olenik, I., Rupp, R., Lenzini, G., Lagerwall, J.P.: High-fidelity spherical cholesteric liquid crystal Bragg reflectors generating unclonable patterns for secure authentication. Sci. Rep. 6, 1–9 (2016). https://doi.org/10.1038/srep26840
Geng, Y., Noh, J., Drevensek-Olenik, I., Rupp, R., Lagerwall, J.: Elucidating the fine details of cholesteric liquid crystal shell reflection patterns. Liq. Cryst. 44(12–13), 1948–1959 (2017)
Geng, Y., Kizhakidathazhath, R., Lagerwall, J.P.F.: Encoding hidden information onto surfaces using polymerized cholesteric spherical reflectors. Adv. Funct. Mater. 31 (2021). https://doi.org/10.1002/adfm.202100399
Goldreich, O.: Foundations of Cryptography, vol. 1. Cambridge University Press, New York, NY, USA (2006)
Gomez-Barrero, M., Maiorana, E., Galbally, J., Campisi, P., Fierrez, J.: Multi-biometric template protection based on homomorphic encryption. Pattern Recogn. 67, 149–163 (2017)
Ivarsson, J., Nilsson, A.: A Review of Hardware Security Modules (2010). https://www.opendnssec.org/wp-content/uploads/2011/01/A-Review-of-Hardware-Security-Modules-Fall-2010.pdf. Accessed Mar 2022
Joshi, M., Mazumdar, B., Dey, S.: Security Vulnerabilities Against Fingerprint Biometric System (2018). arXiv1805.07116, http://arxiv.org/abs/1805.07116
Johnson, D., Menezes, A., Vanstone, S.: The elliptic curve digital signature algorithm (ECDSA). Int. J. Inf. Secur. 1(1), 36–63 (2001). https://doi.org/10.1007/s102070100002
Karabat, C., Kiraz, M.S., Erdogan, H., Savas, E.: THRIVE: threshold homomorphic encryption based secure and privacy preserving biometric verification system. EURASIP J. Adv. Sig. Process. 2015(1), 1–18 (2015). https://doi.org/10.1186/s13634-015-0255-5
Khan, M.A.: Fingerprint image enhancement and minutiae extraction (2011)
Kim, M.S., Lee, G.J., Leem, J.W., Choi, S., Kim, Y.L., Song, Y.M.: Revisiting silk a lens-free optical physical unclonable function. Nature Commun. 13(1), 1–12 (2022). https://doi.org/10.1038/s41467-021-27278-5, https://www.nature.com/articles/s41467-021-27278-5
Laine, K.: Simple encrypted arithmetic library 2.3. 1. Microsoft Research (2017). https://www.microsoft.com/en-us/research/uploads/prod/2017/11/sealmanual-2-3-1.pdf
Lenzini, G., et al.: Security in the shell an optical physical unclonable function made of shells of cholesteric liquid crystals. In: 2017 IEEE Workshop on Information Forensics and Security, WIFS 2017 2018-Janua, pp. 1–6 (2017). https://doi.org/10.1109/WIFS.2017.8267644
Ratha, N., Bolle, R., Pandit, V., Vaish, V.: Robust fingerprint authentication using local structural similarity. In: Proceedings Fifth IEEE Workshop On Applications Of Computer Vision, pp. 29–34 (2000)
National Institute of Standards and Technology SP 800–131A Rev. 2: Transitioning the Use of Cryptographic Algorithms and Key Lengths (2018). https://csrc.nist.gov/publications/detail/sp/800-131a/rev-2/final
Ngo, D., Teoh, A., Goh, A.: Biometric hash high-confidence face recognition. IEEE Trans. Circuits Syst. Video Technol. 16(6), 771–775 (2006). https://doi.org/10.1109/TCSVT.2006.873780
Pradel, G., Mitchell, C.: Privacy-Preserving Biometric Matching Using Homomorphic Encryption. arXiv preprint arXiv:2111.12372 (2021)
Pursell, L., Trimble, S.Y.: Gram-schmidt orthogonalization by Gauss elimination. Am. Math. Mon. 98(6), 544–549 (1991). https://doi.org/10.1080/00029890.1991.11995755
Schneider, T.: Engineering Secure Two-Party Computation Protocols - Advances in Design, Optimization, and Applications of Efficient Secure Function Evaluation. Ph.D. thesis, Ruhr-University Bochum, Germany, Information Sciences (2011). http://thomaschneider.de/papers/S11Thesis.pdf
Schwartz, M., Lenzini, G., Geng, Y., Rønne, P.B., Ryan, P.Y., Lagerwall, J.P.: Cholesteric liquid crystal shells as enabling material for information-rich design and architecture. Adv. Mater. 30(30), 1–19 (2018). https://doi.org/10.1002/adma.201707382
Schwartz, M., et al.: Linking physical objects to their digital twins via fiducial markers designed for invisibility to humans. Multifunctional Mater. 2(4), 1–19 (2021). https://doi.org/10.1088/2399-7532/ac0060
Topcu, B., Karabat, C., Azadmanesh, M., Erdogan, H.: Practical security and privacy attacks against biometric hashing using sparse recovery. EURASIP J. Adv. Sig. Process. 2016(1), 1–20 (2016). https://doi.org/10.1186/s13634-016-0396-1
Torres, W.A.A., Bhattacharjee, N., Srinivasan, B.: Effectiveness of fully homomorphic encryption to preserve the privacy of biometric data. In: Proceedings of the 16th International Conference on Information Integration and Web-based Applications & Services, pp. 152–158 (2014)
Tuyls, P., Akkermans, A.H., Kevenaar, T.A., Schrijen, G.J., Bazen, A.M., Veldhuis, R.N.: Practical biometric authentication with template protection. Lect. Notes Comput. Sci. 3546, 436–446 (2005). https://doi.org/10.1007/11527923_45
Yu, H., Yin, L., Zhang, H., Zhan, D., Qu, J., Zhang, G.: Road distance computation using homomorphic encryption in road networks. CMC-Comput. Mater. Continua 69(3), 3445–3458 (2021)
Acknowledgements
We thank the reviewers for their valuable comments and suggestions. We would also like to acknowledge Prof. Dr. J. Lagerwall for providing the CSRs images. In addition, Mónica Arenas and Georgios Fotiadis would like to thank Dr. Kim Laine, from Microsoft Research, for his responsiveness and valuable comments regarding the BFV homomorphic encryption scheme and its implementation. The authors acknowledge the financial support from the Luxembourg National Research Fund (FNR) on the projects Security in the Shell “SSh” (C17/MS/11688643), No more Fakes “NoFakes” (PoC20/15299666/NOFAKES-PoC) and the CORE project Secure, Quantum-Safe, Practical Voting Technologies “EquiVox” (C19/IS/13643617/EquiVox/Ryan).
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Arenas, M.P., Bingol, M.A., Demirci, H., Fotiadis, G., Lenzini, G. (2022). A Secure Authentication Protocol for Cholesteric Spherical Reflectors Using Homomorphic Encryption. In: Batina, L., Daemen, J. (eds) Progress in Cryptology - AFRICACRYPT 2022. AFRICACRYPT 2022. Lecture Notes in Computer Science, vol 13503. Springer, Cham. https://doi.org/10.1007/978-3-031-17433-9_18
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